The molecular "spring constant" can be different for different directions
If , then the material has a single optics axis and is called crystal
3
Microscopic Lorentz Oscillator Model
In the transparent regime …
4
Birefringent Materials o-ray
no
e-ray
ne
Image by Arenamotanus http://www.flickr.com/photos/ arenamontanus/2756010517/ on flickr
All transparent crystals with non-cubic lattice structure are birefringent. 5
Polarization Conversion Linear to Circular
inside
Polarization of output wave is determined by…
6
Quarter-Wave Plate left circular output
Circularly polarized output
45o
linearly polarized input
Example: If we are to make quarter-wave plate using calcite (no = 1.6584, ne = 1.4864), for incident light wavelength of λ = 590 nm, how thick would the plate be ?
2π
λ
no − ne d =
π
d=
2
7
λ
4 no − ne
d = 0.857 µm
3D Movies Technology Polarizer A Left eye source
Right eye source
Film or digital projector
Film or digital projector
Polarizer B Image by comedy_nose http://www.flickr.com/photos/ comedynose/4482682966/ on flickr
Which approach is better ? Linear or circular polarization ? 8
A linearly polarized wave can be represented as a sum of two circularly polarized waves
CIRCULAR
LINEAR
9
CIRCULAR
Circular Birefringence But as the two circular polarizations of light travel through the circular birefringence material at different speeds, they will be phase shifted when they exit the medium
10
Circular Birefringence
nleft ≠ nright
Chiral molecules… …different interactions with left- and rightcircular polarizations 11
All images in the public domain
Polarization Rotation with Circular Birefringence
x-polarized
y-polarized
-
12
Interleaved 3D Movies
Shuttered/ switching polarizer Left eye source
High frame rate projector
Right eye source
Image by comedy_nose http://www.flickr.com/photos/ comedynose/4482682966/ on flikr
13
Liquid Crystal Displays Circular birefringence
E=0
NO circular birefringence
E=0
14
States of Matter Solid (crystalline): incompressible, no flow under shear crystal = periodic in space
Liquid Crystal: incompressible, flows under shear long range order
Liquid:
Gas:
incompressible, flows under shear very short range order
compressible 15
Steemers, SID Seminar Notes 1994.
Liquid Crystal Structure Crystal
Increasing temperature
Liquid
Vapor
Liquid Crystal melting point
Nematic liquid crystal - Molecules tend to be parallel but their positions are random - Long range orientation order
clearing point
Smetic liquid crystal - Positional order in 1-D - Long range orientational order 16
Temperature
Cholsteric liquid crystal - Distorted form of the nematic phase in which the orientation undergoes helical rotation - Chiral molecules
Twisting Liquid Crystals LC ordering is determined by anisotropic boundary conditions (grooves) Light
S
polarizers
Alignment layers
17
Voltage
6.007 Lab Pixel Polarizer glass ITO PVA Liquid crystal
LC dielectric anisotropy allows control of molecular orientation by the external E-field. Molecules rotate to minimize stored energy
E=0
What is the physical reason for LC rotation ? 19
Figure 2.16 from Hearn and Baker
Anisotropic Dielectric Constant A
+ + + + + + + + + + + + + + + + + + +
d
-
-
-
-
-
-
-
-
-
+
+
+
+
+
+
+
+
+
- - - - - - - - - - - - - - - - -
A
d
+ + + + + + + + + + + + + + + + + + + -
+
-
+
-
+
-
+
-
+
- - - - - - - - - - - - - - - - 20
Energy Method for LC A
+ + + + + + + + + + + + + + + + + + +
d
-
-
-
-
-
-
-
-
-
+
+
+
+
+
+
+
+
+
Stored energy …
1 1 Q2 WE = D ⋅ E = 2 2 C (θ )
- - - - - - - - - - - - - - - - -
A
d
Force acts to increase capacitance …
+ + + + + + + + + + + + + + + + + + + -
-
-
+
+
+
-
∂WE f = − ∂θ Q
-
+
+
- - - - - - - - - - - - - - - - -
(
)
Dz = ε || cos θ + ε ⊥ sin θ E 2
2
21
Electro-Optic Response of Twisted Nematic Liquid Crystal Cell
Relative Transmission
T=90%
T=10% Applied Voltage LC cell is 5 μm to 10 μm thick At 3 V applied dc-bias E–field is 3 to 6 kV/cm 22
Relative Transmission
Applied voltage
Transient Response of Twisted Nematic Liquid Crystal Cell
Time
Tfall
Trise
23
The response is not instantaneous. This limits the refresh rate!
Reflective LCD Display … illuminated by external light (sunlight)
6 5
Reflective surface to send light back to viewer.
Horizontal filter film to block/allow through light.
4
Glass substrate with common electrode film (ITO) with horizontal ridges to line up with the horizontal filter. 3 Twisted nematic liquid crystals.
2 Glass substrate with ITO electrodes. The shapes of these electrodes will
1
determine the dark shapes that will appear when the LCD is turned on. Vertical ridges are etched on the surface so the liquid crystals are in line with the polarized light. Vertical filter film to polarize the light as it enters. 24
Display Addressing DIRECTLY ADDRESSED DISPLAY
MATRIX DISPLAY HI LO
Common Electrode
v
Segmented Electrode DISABLE ENABLE
Cathode Rows
Active Layers
Example: for X=640 x Y480 panel of emissive elements direct addressing 2 x 640 x 480 = 614,400 (2*X*Y) wires matrix addressing 640 + 480 = 1120 (X+Y) wires 25
Substrate Anode Columns
Fluorescent backlight
LCD Display Cross-Section
Vertical Polarizing filter
Column Addressing line
Top polarizer Retardation film Top glass Column electrodes Liquid crystal Row electrodes Over coating Color filter
Row Addressing line
Bottom glass Retardation film Bottom polarizer Backlight
Subpixel electrode
Example of a Color Filter (green)
Transistor Pixel ON
Glass plate Liquid crystal layer 26
Front plate Horizontal Polarizing filter
LCD Backlight • Consists of light source, reflector, and diffuser • Goals are compactness, high efficiency, uniformity, long life
Retina has FOUR types of Receptors: 120 million Rods – brightness 6 million Cones – color B 5-10% (“S-cones”) G ~30% (“M-cones”) R ~60% (“L-cones”)
Cone Rod
The Neural Structure of the Retina 29
Spectral Sensitivity of Cones S Relative Sensitivity
• L-cones have peak absorption at λ~560 nm • M-cones have peak absorption at λ~530 nm • S-cones have peak absorption at λ~430 nm • The three cones have broad sensitivity curves with a lot of overlap
1.5
L
1.0
0.5
0
– Light at 550 nm will evoke response from L- and Mcones but much weaker response from S-cones
M
400
500
600
Wavelength [nm]
30
700
LCD under a Magnifier
31
conductive coating
Polymer Dispersed LCDs – Privacy Glass
suspension Suspended li+quid particle -
Image by University of Michigan MSIS http://www.flickr.com/photos/umichmsis/6443313259/ on flickr
+
-
OFF
OFF
• A standard meeting room with some privacy protection • Polymer dispersed LCDs allow for changeable transparency
ON
32
Electrochromic Windows
When switched “OFF” and electrochromic window remains transparent. When switched “ON” voltage drives the ions from the ion storage layer, through the ion conducting layer and into the electrochromic layer. Oxidation reaction -- a reaction in which molecules in a compound lose an electron changes the dielectric properties of the electrochromic layer, which now absorbs the incident light, are what allow it to change from opaque to transparent. It's these ions that allow it to absorb light. By shutting off the voltage, the ions are driven out of the electrochromic layers and into the ion storage layer. When the ions leave the electrochromic layer, the window regains its transparency.
- Shift of the Lorentz Oscillator - change Optical Absorption
Electrochromic layer
OFF
Conductive layers
+ + + + +
+ +
Image by Bitboy http://www.flickr.com/photos/bitbo y/2388546266// on flickr
Ion storage Conductor
Ion conductor/ Electrolyte
-
ON
33
A rear view mirror with an electrochromic layer for dimming during night time use
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6.007 Electromagnetic Energy: From Motors to Lasers Spring 2011
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